Solve the following quadratic equation for all values of xx in simplest form.
5, left parenthesis, x, squared, minus, 7, right parenthesis, minus, 1, equals, 9
5(x 
2
 −7)−1=
9
Answer
Attempt 1 out of 2

We are given the quadratic equation:

\[
5(x^2 - 7) - 1 = 9
\]

### Step 1: Simplify the equation
Distribute the \(5\) on the left-hand side:

\[
5(x^2 - 7) = 5x^2 - 35
\]

So the equation becomes:

\[
5x^2 - 35 - 1 = 9
\]

Simplify the left-hand side:

\[
5x^2 - 36 = 9
\]

### Step 2: Isolate the quadratic term
Add \(36\) to both sides of the equation to isolate the \(x^2\) term:

\[
5x^2 = 9 + 36
\]

\[
5x^2 = 45
\]

### Step 3: Solve for \(x^2\)
Divide both sides by \(5\):

\[
x^2 = \frac{45}{5}
\]

\[
x^2 = 9
\]

### Step 4: Solve for \(x\)
Take the square root of both sides:

\[
x = \pm \sqrt{9}
\]

\[
x = \pm 3
\]

### Final Answer:
The solutions to the equation are:

\[
x = 3 \quad \text{or} \quad x = -3
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you solve a quadratic equation by factoring?
2. What are the properties of square roots?
3. How do you check if the solution to a quadratic equation is correct?
4. Can a quadratic equation have no real solution?
5. What are the different methods to solve a quadratic equation?

**Tip:** Always check your solutions by substituting them back into the original equation to verify correctness.

Solve the following quadratic equation for all values of x in simplest form: 5(x^2 - 7) - 1 = 9

Learn how to solve the quadratic equation 5(x^2 - 7) - 1 = 9 using algebraic simplification and the square root property. Follow the step-by-step solution that includes isolating the quadratic term and taking square roots to find x = ±3. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation